Modeling Water Uptake by Plant Roots

Abstract

A mathematical model is developed that describes water uptake from soil by the roots of transpiring plants. Starting from a one-dimensional Richards equation with a root water extraction term, a partial differential equation predicting the moisture content in the soil profile is formulated. There are many expressions in literature that predict water extraction by plant roots, each one of them having its own merits and demerits. This study proposes a simple model with a linear root water extraction term that varies with time. The model also incorporates a sinusoidal root growth function that takes into account the root growth with time. The flow equation is subjected to a boundary condition that signifies the potential evaporation or the applied water (head) during the irrigation application time at the top boundary. The simulated model without the extraction function is validated by comparing the model results with experimental studies predicting soil moisture content for both a homogeneous and a layered medium. A linear root water extraction term is later adopted in the model, and a hypothetical case is simulated to compute the water uptake by plant roots. The comparison in all test cases was found to be reasonably good.